Atkin-Lehner |
2+ 3+ 5- 23+ |
Signs for the Atkin-Lehner involutions |
Class |
690d |
Isogeny class |
Conductor |
690 |
Conductor |
∏ cp |
4 |
Product of Tamagawa factors cp |
deg |
144 |
Modular degree for the optimal curve |
Δ |
-285660 = -1 · 22 · 33 · 5 · 232 |
Discriminant |
Eigenvalues |
2+ 3+ 5- 4 2 4 -6 -4 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-12,-36] |
[a1,a2,a3,a4,a6] |
j |
-217081801/285660 |
j-invariant |
L |
1.2098350004653 |
L(r)(E,1)/r! |
Ω |
1.2098350004653 |
Real period |
R |
1 |
Regulator |
r |
0 |
Rank of the group of rational points |
S |
1 |
(Analytic) order of Ш |
t |
2 |
Number of elements in the torsion subgroup |
Twists |
5520bg1 22080bb1 2070p1 3450y1 |
Quadratic twists by: -4 8 -3 5 |